Example 2. Use the forward-substitution method to solve the lower-triangular linear system  [Graphics:Images/BackSubstitutionMod_gr_88.gif].  
Use the menu "Input" then submenu "Create Table/Matrix/Palette" to enter matrix A and vector B.

Solution 2.

[Graphics:../Images/BackSubstitutionMod_gr_89.gif]

Then perform forward-substitution.

[Graphics:../Images/BackSubstitutionMod_gr_90.gif]
[Graphics:../Images/BackSubstitutionMod_gr_91.gif]

Verify the solution.

[Graphics:../Images/BackSubstitutionMod_gr_92.gif]

[Graphics:../Images/BackSubstitutionMod_gr_93.gif]

[Graphics:../Images/BackSubstitutionMod_gr_94.gif]

[Graphics:../Images/BackSubstitutionMod_gr_95.gif]

[Graphics:../Images/BackSubstitutionMod_gr_96.gif]

To do it in decimals, you can enter decimal values in the matrix and vector.

[Graphics:../Images/BackSubstitutionMod_gr_97.gif]

[Graphics:../Images/BackSubstitutionMod_gr_98.gif]

[Graphics:../Images/BackSubstitutionMod_gr_99.gif]

But why require yourself to type all those decimal points ?
The same thing could be accomplished by using the convert to numerical function, that's the reserved word  [Graphics:../Images/BackSubstitutionMod_gr_100.gif].

[Graphics:../Images/BackSubstitutionMod_gr_101.gif]

[Graphics:../Images/BackSubstitutionMod_gr_102.gif]

[Graphics:../Images/BackSubstitutionMod_gr_103.gif]


[Graphics:../Images/BackSubstitutionMod_gr_104.gif]
[Graphics:../Images/BackSubstitutionMod_gr_105.gif] [Graphics:../Images/BackSubstitutionMod_gr_106.gif] [Graphics:../Images/BackSubstitutionMod_gr_107.gif]
[Graphics:../Images/BackSubstitutionMod_gr_108.gif]

Verify the solution.

[Graphics:../Images/BackSubstitutionMod_gr_109.gif]


[Graphics:../Images/BackSubstitutionMod_gr_110.gif]

[Graphics:../Images/BackSubstitutionMod_gr_111.gif]

[Graphics:../Images/BackSubstitutionMod_gr_112.gif]

[Graphics:../Images/BackSubstitutionMod_gr_113.gif]

 

 

 

 

 

 

 

 

 

 

 

 

(c) John H. Mathews 2003